A stable high-order finite difference scheme for the compressible Navier-Stokes equations

  • Authors:

  • Magnus Svärd;Jan Nordström

  • Affiliations:

  • Centre of Mathematics for Applications, University of Oslo, P.O. Box 1053, Blindern, N-0316 Oslo, Norway;Department of Computational Physics, The Swedish Defense Research Agency, SE-164 90 Stockholm, Sweden and Department of Information Technology, Uppsala University, SE-751 05 Uppsala, Sweden and De ...

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2008

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Abstract

A stable wall boundary procedure is derived for the discretized compressible Navier-Stokes equations. The procedure leads to an energy estimate for the linearized equations. We discretize the equations using high-order accurate finite difference summation-by-parts (SBP) operators. The boundary conditions are imposed weakly with penalty terms. We prove linear stability for the scheme including the wall boundary conditions. The penalty imposition of the boundary conditions is tested for the flow around a circular cylinder at Ma=0.1 and Re=100. We demonstrate the robustness of the SBP-SAT technique by imposing incompatible initial data and show the behavior of the boundary condition implementation. Using the errors at the wall we show that higher convergence rates are obtained for the high-order schemes. We compute the vortex shedding from a circular cylinder and obtain good agreement with previously published (computational and experimental) results for lift, drag and the Strouhal number. We use our results to compare the computational time for a given for a accuracy and show the superior efficiency of the 5th-order scheme.